We present results of a study of frequency stabilization of a diode laser (λ = 780 nm) using the Doppler-free dichroic lock (DFDL) technique and its use for laser cooling of atoms. Quantitative measurements of frequency stability were performed and the Allan variance was found to be 6.9 × 10¹¹ for an averaging time of 10 s. The frequency-stabilized diode laser was used to obtain the trapping beams for a magneto-optic trap (MOT) for Rb atoms. Using the DFDL technique, the laser frequency could be locked over a wide range and this enabled measurement of detuning dependence of the number and temperature of cold atoms using a relatively simple experimental set-up.